### Math ClubHilbert's 7th ProblemKeith Conrad (UConn)

Wednesday, October 9, 2019
5:45pm – 6:35pm

Storrs Campus
Monteith 226

A number that is the root of a nonconstant polynomial with integer coefficients is called algebraic (it is related to integers by algebraic operations) and numbers that are not algebraic are called transcendental (they "transcend" the tools of algebra). For example, $$\sqrt{2}$$ is algebraic since it is a root of $$x^2-2$$, while $$\pi$$ is transcendental. Showing $$\pi$$ is transcendental is very hard!

Hilbert's 7th problem asks about the transcendence of certain exponential expressions $$a^b$$, such as $$2^{\sqrt{2}}$$. We will explain the background to this problem, how the solution turned out, and sketch the argument that a particular number (not $$\pi$$) is transcendental.

Note: Free pizza and drinks!

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